Paano kaya natin paghiwalayin ang karton at plastik?

No. In this sentence, kaya is a particle, not the adjective meaning able.

Here it adds a feeling of:

• wondering
• tentativeness
• possibility
• softening

So Paano kaya natin... feels like:

• How could we... ?
• How might we... ?
• I wonder how we can...

Without kaya, the question would sound more direct:

• Paano natin paghiwalayin ang karton at plastik?

Because this verb pattern uses the actor in the genitive form, and natin is the inclusive genitive form of we.

A very simple way to think about it:

• tayo = we in a form often used when the actor is marked as the main topic/focus
• natin = we / us / our in a genitive form, which also gets used to mark the actor in many non-actor-focus sentences

In this sentence, natin means we as the ones doing the separating.

Also, natin is inclusive, so it includes the listener:

• natin = we, including you
• namin = we, not including you

So the sentence is asking something like How can we separate the cardboard and plastic?, with the listener included.

Because Filipino pronouns do more than one job depending on the sentence structure.

Natin can mean:

• our in a possessive phrase, as in bahay natin = our house
• we/us in certain verb constructions, as in this sentence

Here it is not showing possession. It is marking the people doing the action. So natin is best understood as we.

The root is hiwalay, which has the basic idea of separate, apart, or separated.

Paghiwalayin is an affixed verb form meaning roughly:

• to separate
• to cause to be separate
• to separate from each other

So in this sentence, paghiwalayin means separate the cardboard and plastic from each other.

A useful thing to remember is that Filipino verbs often carry a lot of meaning in their affixes, so it is better to learn paghiwalayin as a whole verb form, not just try to translate each piece mechanically.

Because in this kind of sentence, the thing affected by the action is marked with ang.

That is one of the big differences between Filipino and English:

• English usually centers grammar around subject vs. object
• Filipino often centers grammar around focus/topic marking

Here:

• natin = the doer
• ang karton at plastik = the thing being separated

So ang is marking the item or items under discussion as the focused element of the clause.

Not exactly.

Sometimes ang can line up with English the in translation, but it is not just an article. Its main job is grammatical marking.

In this sentence, ang is marking the noun phrase karton at plastik as the focused/topic-marked part of the clause. Depending on context, that phrase could be understood as:

• specific cardboard and plastic
• cardboard and plastic in general
• the cardboard and plastic we are dealing with

So it is better not to treat ang as a simple one-to-one equivalent of the.

Because karton at plastik is one coordinated noun phrase.

In English, it is the same idea as:

• the cardboard and plastic

You do not need to repeat the marker before the second noun when both nouns share the same role in the sentence.

So:

• ang karton at plastik = natural

You may sometimes see repeated markers in other contexts for emphasis or clarity, but here one ang is the normal choice.

Because this sentence uses a pattern that names both things being separated:

• paghiwalayin ang X at Y = separate X and Y from each other

If you want a structure closer to English separate X from Y, Filipino often uses another verb pattern, for example:

• Ihiwalay ang karton sa plastik.

So both ideas are possible, but they are built differently:

• Paghiwalayin ang karton at plastik.
  Separate the cardboard and plastic from each other.

• Ihiwalay ang karton sa plastik.
  Separate the cardboard from the plastic.

Because Filipino often puts:

1. the question word first
2. particles very early
3. short pronouns near the front as well

So the order:

• Paano = question word
• kaya = particle
• natin = short pronoun
• paghiwalayin... = verb

is very natural.

This is one reason word-for-word English ordering usually does not work well in Filipino. The sentence is not trying to copy English structure; it is following normal Filipino placement rules.

Paghiwalayin here works like a base or infinitive-like form: to separate.

After words like paano, Filipino often uses this kind of neutral verb form when talking about method or possibility:

• Paano ... paghiwalayin ... = How to separate ... / How can we separate ...

A form like paghihiwalayin is more clearly future or contemplated:

• Paano natin paghihiwalayin ang karton at plastik?
  How are we going to separate the cardboard and plastic?

So the given sentence sounds a bit more like discussing the method, while the longer form can sound more explicitly future-oriented.

They overlap, but they are not exactly the same in feel or pattern.

A simple way to remember it:

• paghiwalayin often means separate two things from each other
• ihiwalay often means set one thing apart from another thing

Examples:

• Paghiwalayin ang karton at plastik.
  Separate the cardboard and plastic from each other.

• Ihiwalay ang karton sa plastik.
  Separate the cardboard from the plastic.

In real-life use, both can work in sorting or recycling contexts, but the grammar around them is different.

Yes. They are familiar-looking because they are borrowed forms used naturally in Filipino.

• karton = cardboard / carton
• plastik = plastic

Filipino has many everyday loanwords, especially for common materials and objects. Even when the words look familiar to an English speaker, they still behave like normal Filipino nouns inside Filipino grammar.